Question

3400 dollars is placed in an account with an annual interest rate of 8.25%. how much will be in the account after 25 years, to the nearest cent?

Explanation:

Step1: Identify the formula

We use the compound - interest formula (assuming compound interest, if it's simple interest, the formula is \(A = P(1+rt)\); but usually, for long - term savings, compound interest is more common. The compound - interest formula is \(A=P(1 + r)^t\), where:

• \(P\) is the principal amount (the initial amount of money), here \(P = 3400\) dollars.
• \(r\) is the annual interest rate (in decimal form), so \(r=\frac{8.25}{100}=0.0825\).
• \(t\) is the number of years, here \(t = 25\).

Step2: Substitute the values into the formula

Substitute \(P = 3400\), \(r=0.0825\) and \(t = 25\) into the formula \(A = P(1 + r)^t\):
\(A=3400\times(1 + 0.0825)^{25}\)

First, calculate \((1 + 0.0825)=1.0825\). Then calculate \(1.0825^{25}\).
Using a calculator, \(1.0825^{25}\approx7.0702\) (you can calculate this by repeatedly multiplying \(1.0825\) twenty - five times or using the power function on a calculator).

Then, \(A = 3400\times7.0702\)
\(A=3400\times7.0702 = 24038.68\) (rounded to the nearest cent)

Answer:

\(24038.68\) dollars